Magnetic Modification of Black Hole Photospheres with Image Contraction, Efficiency Shifts and Redshift Boosts in Schwarzschild-Bertotti-Robinson Spacetime

Abstract

We investigate the optical and radiative signatures of an accretion disk around a Schwarzschild black hole (BH) immersed in a uniform magnetic field. The spacetime geometry is described by the Schwarzschild-Bertotti-Robinson (SBR) metric, which represents the non-rotating sector of the recently discovered Kerr-Bertotti-Robinson exact solution to the Einstein-Maxwell equations. We begin with the study of null geodesics and demonstrate that the self-consistent magnetic field fundamentally alters photon propagation, causing an expansion of light bundles relative to the Schwarzschild case due to modified initial conditions in the orbital equation. We then compute the magnetic field-dependent shifts of key characteristic radii: the event horizon ($r_h$), photon sphere ($r_{ph}$), and innermost stable circular orbit ($r_{ISCO}$). We find that all three increase monotonically with field strength $B$, revealing a magnetic amplification of the effective gravitational field. For $B=0.05$, we find that the lensed emission bands contract to a narrower impact parameter range, $b\in(4.976,5.149)\cup(5.19,6.128)$. Employing ray-tracing formalism, we construct observed accretion disk images and quantify magnetic modifications, showing that the direct image contracts while maximum energy flux, radiation temperature, and redshift factor are enhanced. Complementing these numerical findings, we develop an analytical framework for the accretion disk dynamics. We derive the modified Keplerian frequency $Ω_K$, along with the specific energy $E$ and angular momentum $L$ for circular orbits. From these, we obtain the exact ISCO radius $r_{\text{ISCO}}$, which shows an outward shift. This outward shift reveals that the radiative efficiency decreases dramatically with increasing magnetic field strength $B$. For $β= BM \sim 0.1$, the efficiency drops by approximately $91\%$.

Figures (9)

• Figure 1: The plots demonstrate photon trajectories near the SBR BH for different values of $B$. The colored curves depict separate ranges of the impact parameter $b$: gray for $3<b\leq5$, red for $5<b\leq5.5$, and orange for $b>5.5$. The black dashed ring denotes the photon-sphere location.
• Figure 2: Schematic illustration of the coordinate system employed to construct the accretion disk image Luminet1979XamidovAccretion2025.
• Figure 3: The plots illustrate image formation diagrams for different values of the disk radii $R$ at fixed $B=0.03$ (left panel) and for different values of the magnetic field $B$ at fixed radius $R=15$ (right panel).
• Figure 4: Direct (solid curves) and secondary (dashed curves) images of the accretion disk around the SBR BH for distinct disk radii $R$. The plots in each column correspond to different values of the magnetic field $B$, while rows correspond to a fixed inclination angle $\theta_0$.
• Figure 5: The radial distributions of energy flux $F(r)$ (left) and temperature $T(r)$ (right) on the accretion disk for different values of magnetic field $B$.